Question

a yogurt company claims that it prints a free yogurt coupon under a randomly selected 20% of its lids. a loyal customer purchases 85 yogurt cups, and records whether each was a winner. after consuming all 85 cups, he is disappointed to see that only 12 (14.1%) of his yogurt cups contained coupon codes. he performs a 99% confidence interval for the proportion of yogurt cups containing coupon codes, obtaining (0.044, 0.238). what conclusion can the customer draw about the yogurt companys claim?
the companys claim may be justified because 0.2 is in the confidence interval.
the companys claim is definitely justified because 0.2 is in the confidence interval.
the companys claim is not justified because the upper endpoint of the confidence interval is 0.238.
the companys claim is not justified because 12 out of 85 (0.141) is far less than 0.2.

Explanation:

A 99% confidence interval means we are 99% confident the true proportion of coupon-containing lids lies within (0.044, 0.238). The company's claimed proportion is 0.2, which falls inside this interval. Confidence intervals do not prove a claim is definitely true, only that the claim is consistent with the observed data.

Answer:

The company's claim may be justified because 0.2 is in the confidence interval.